Question

1. Show that the optimal efficiency of a cylindrical friction pump occurs when α=-1.0

2. Calculate the maximum possible efficiency of a friction pump

Notice: η = Power Attained / Power Expended

Answer 1

Answer 2.

When we speak of the efficiency of any machine, we are simply referring to how well it can convert one form of energy to another. If one unit of energy is supplied to a machine and its output, in the same units of measure, is one-half unit, its efficiency is 50 percent.

As simple as this may seem, it can still get a bit complex because the units used by our English system of measurement can be quite different for each form of energy. Fortunately, the use of constants brings equivalency to these otherwise diverse quantities.

A common example of such a machine is the heat engine, which uses energy in the form of heat to produce mechanical energy. This family includes many members, but the internal combustion engine is one with which we are all familiar. Although this machine is an integral part of our everyday lives, its effectiveness in converting energy is far less than we might expect.

The efficiency of the typical automobile engine is around 20 percent. To put it another way, 80 percent of the heat energy in a gallon of gasoline does no useful work. Although gas mileage has increased somewhat over the years, that increase has as much to do with increased mechanical efficiency as increased engine efficiency itself.

Diesel engines do a better job but still max out around 40 percent. This increase is due, primarily, to its higher compression ratio and the fact that the fuel, under high pressure, is injected directly into the cylinder

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PUMPS

Centrifugal Pump Efficiency—What Is Efficiency?

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by Joe Evans, Ph.D.
January 20, 2012
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Editor's Note: This is the first in a six-part series on centrifugal pump efficiency. For other articles in this series, click here.

In this multi-part series, we will investigate several aspects of centrifugal pump efficiency. First, I will define efficiency and give some examples. Next, I will examine some of the design criteria that ultimately dictate the efficiency exhibited by a particular pump.

I will also try to make that somewhat nebulous quantity, known as specific speed, more meaningful. I will illustrate its effect on the shape of a pump’s performance curve and overall pump efficiency.

Next, I will explain the contributions of individual pump components to a pump’s overall efficiency and show why the combined efficiency of a pump and its driver is the product, not the average, of the two efficiencies.

How pump efficiency can be preserved by changing impeller speed rather than reducing it diameter will also be examined. Then I will compare the value of peak efficiency versus the breadth of efficiency over a range of flow. The discussion will end with the importance, or sometimes unimportance, of efficiency as it relates to a particular application or process.

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What Is Pump Efficiency?

When we speak of the efficiency of any machine, we are simply referring to how well it can convert one form of energy to another. If one unit of energy is supplied to a machine and its output, in the same units of measure, is one-half unit, its efficiency is 50 percent.

As simple as this may seem, it can still get a bit complex because the units used by our English system of measurement can be quite different for each form of energy. Fortunately, the use of constants brings equivalency to these otherwise diverse quantities.

A common example of such a machine is the heat engine, which uses energy in the form of heat to produce mechanical energy. This family includes many members, but the internal combustion engine is one with which we are all familiar. Although this machine is an integral part of our everyday lives, its effectiveness in converting energy is far less than we might expect.

The efficiency of the typical automobile engine is around 20 percent. To put it another way, 80 percent of the heat energy in a gallon of gasoline does no useful work. Although gas mileage has increased somewhat over the years, that increase has as much to do with increased mechanical efficiency as increased engine efficiency itself.

Diesel engines do a better job but still max out around 40 percent. This increase is due, primarily, to its higher compression ratio and the fact that the fuel, under high pressure, is injected directly into the cylinder.

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In the pump industry, much of the work involves two extremely simple, yet efficient, machines—the centrifugal pump and the AC induction motor. The centrifugal pump converts mechanical energy into hydraulic energy (flow, velocity and pressure), and the AC motor converts electrical energy into mechanical energy.

Many medium and larger centrifugal pumps offer efficiencies of 75 to 93 percent and even the smaller ones usually fall into the 50 to 70 percent range. Large AC motors, on the other hand, approach an efficiency of 97 percent, and any motor—ten horsepower and above—can be designed to break the 90 percent barrier.

The overall efficiency of a centrifugal pump is simply the ratio of the water (output) power to the shaft (input) power and is illustrated by the equation below:

Ef = PW / PS

Where:

Ef= efficiency

Pw= the water power

Ps= the shaft power

In the U.S., Ps is the power provided to the pump shaft in brake horsepower (BHP) and Pw is:

Pw = (Q x H) / 3960

Where:

Q= Flow (gallons per minute—GPM)

H= Head (feet)

The constant (3,960) converts the product of flow and head (GPM-feet) into BHP. These equations predict that a pump that produces 100 GPM at 30 feet of head and requires 1 BHP will have an overall efficiency is 75.7 percent at that flow point.